Answer :
We start with the expression
[tex]$$
\frac{2x^2 - 6x^2}{2x^3}.
$$[/tex]
1. Combine like terms in the numerator:
[tex]$$2x^2 - 6x^2 = -4x^2.$$[/tex]
The expression now becomes:
[tex]$$\frac{-4x^2}{2x^3}.$$[/tex]
2. Simplify the fraction by separating the numerical coefficients and the powers of [tex]$x$[/tex]:
[tex]$$\frac{-4}{2} \cdot \frac{x^2}{x^3}.$$[/tex]
3. Divide the coefficients:
[tex]$$\frac{-4}{2} = -2.$$[/tex]
4. Simplify the powers of [tex]$x$[/tex] using the law of exponents [tex]$\frac{x^a}{x^b} = x^{a-b}$[/tex]:
[tex]$$\frac{x^2}{x^3} = x^{2-3} = x^{-1} = \frac{1}{x}.$$[/tex]
5. Multiply the simplified parts together:
[tex]$$-2 \cdot \frac{1}{x} = -\frac{2}{x}.$$[/tex]
Thus, the simplified expression is
[tex]$$
-\frac{2}{x}.
$$[/tex]
[tex]$$
\frac{2x^2 - 6x^2}{2x^3}.
$$[/tex]
1. Combine like terms in the numerator:
[tex]$$2x^2 - 6x^2 = -4x^2.$$[/tex]
The expression now becomes:
[tex]$$\frac{-4x^2}{2x^3}.$$[/tex]
2. Simplify the fraction by separating the numerical coefficients and the powers of [tex]$x$[/tex]:
[tex]$$\frac{-4}{2} \cdot \frac{x^2}{x^3}.$$[/tex]
3. Divide the coefficients:
[tex]$$\frac{-4}{2} = -2.$$[/tex]
4. Simplify the powers of [tex]$x$[/tex] using the law of exponents [tex]$\frac{x^a}{x^b} = x^{a-b}$[/tex]:
[tex]$$\frac{x^2}{x^3} = x^{2-3} = x^{-1} = \frac{1}{x}.$$[/tex]
5. Multiply the simplified parts together:
[tex]$$-2 \cdot \frac{1}{x} = -\frac{2}{x}.$$[/tex]
Thus, the simplified expression is
[tex]$$
-\frac{2}{x}.
$$[/tex]
